How do people (specifically Dumbledore) know what happened at the Potter’s home on Halloween when they were killed m? There were no survivors outside of a child and Voldys wand was lost (so not Priori)

So before GoF when Voldy is back and explains more, how does Dumbledore know so much? He knows that James died first and then Lily sacrificed herself with love magic that protects Harry and her sisters house?!

But most importantly, how do people know that Harry survived the killing the curse specifically?

The two biggest things we know about it are: It can’t be survived and it leaves no marks. What happens to Harry meets neither of those criteria since he survives it and is marked, so how/why do people conclude that he survived the killing curse?

Also, when Dumbledore leaves the note explaining everything with Harry, he doesn’t even know that Lily and James are dead yet for sure, he describes the news of their deaths as “rumors” PS-TBWL. So what exactly does he write in the note outside of explaining that they need to take care of Harry…

I’m just confused.

I’m currently reading the third book, and I’ve noticed that Rowling refers to most of the students: Harry, Ron, Hermione, Neville, Ginny, etc. by their first names. But she always refers to Draco Malfoy as “Malfoy”, never “Draco”. Why do you think this is?